Tutorial Track
J. Cummings: Singular cardinal combinatorics
The tutorial will focus on the combinatorics of singular cardinals and their successors, with a special emphasis on compactness phenomena.
M. Hušek: Large cardinals in general topology
Influence of some large cardinals on results in topological structures will be discussed. Mainly Ulam measurable cardinal, sequential cardinal and their "higher" concepts (measurable and submeasurable cardinals) will be considered. For topological structures we take topological spaces, uniform spaces, topological groups, topological linear spaces and their nice subcategories. Among the properties discussed are commutations of extensions with products, simplicity of some classes of structures, sequential continuity versus continuity and productivity of special classes of structures. One of the main tools is factorization of mappings defined in products. In some factorizations $\lambda$-strongly compact cardinals will be used.
W. Kubiś: Generic structures
Generic structures are mathematical objects with rich automorphism groups, arising as limits of special sequences. These objects can also be described by the existence of a winning strategy in a natural infinite game where two players alternately choose bigger and bigger structures of the same type.
The theory of generic structures originates from the work of Roland Fraı̈ssé in 1954 and for a long time it was considered to be part of model theory. On the other hand, one of the first generic structures was discovered by Urysohn: A universal ultrahomogeneous Polish metric space. As it happens, generic objects give rise to examples of Polish groups with very interesting dynamics.
The purpose of this tutorial is to present the theory of generic structures, with selected applications and examples from several areas of mathematics.
J. Lopez-Abad: Extremely amenable automorphism groups
The goal of this mini course is to present the main points in the study of the topological dynamics of topological groups when represented as automorphism groups of approximate ultrahomogeneous metric structures. More particularly, we will discuss:
- Fraïssé and metric Fraïssé correspondence for (approximate) ultrahomogeneous structures (AuH).
- Representation of polish groups as automorphism groups $\mathrm{Aut}(\mathcal M)$ of (AuH) structures $\mathcal M$.
- The Kechris–Pestov–Todorcevic (KPT) correspondence between extremely amenable groups of automorphisms of (AuH) structures and the approximate Ramsey property.
- The computation of universal minimal flows.
- Examples, including
- $\mathrm{Aut}(\mathbb Q,<)$,
- $\mathrm{Aut}(\mathbb B)$, where $\mathbb B$ is the countable atomless boolean algebra,
- $\mathrm{Aut}(\mathbb G)$, where $\mathbb G$ is the Gurarij space,
- $\mathrm{Aut}(L_p[0,1])$.
Research Track
| Speaker | Title | Abstract/Slides |
|---|
| Viera Šottová | The first sketch: $\mathcal{N}$ with respect to ideals on $\omega$ | slides |
| Szymon Żeberski | Superperfect Mycielski | slides |
| Serhii Bardyla | Dense and closed subsets of compact-like topological spaces | abstract slides |
| Adam Bartoš | Crookedness and almost homogeneity in categories of compacta | abstract slides |
| Judyta Bąk | On the productivity of the countable chain condition | slides |
| Mariam Beriashvili | Applications of Mazurkiewicz type sets in the study of measurability properties of sets and functions | abstract slides |
| José Antonio Corona | Open colorings | abstract slides |
| Cesar Corral | Uniformization properties of ladder systems under MA(S) | abstract slides |
| Matheus Duzi Ferreira Costa | Topological Games of Bounded Selections | abstract slides |
| Mirna Dzamonja | Logics compact at singular cardinals | slides |
| Monroe Eskew | Elementary embeddings and correctness | abstract slides |
| Miha Habič | Some results on ultrapower capturing | abstract slides |
| K P Hart | You Choose | abstract slides |
| Radek Honzik | Projective wellorder and the tree property | abstract slides |
| Eliza Jabłońska | On $n$-fold sum of a non-flat continuum | abstract slides |
| Michał Korch | Generalized Egorov's statement for ideals | abstract slides |
| Ziemowit Kostana | On countably saturated linear orders | abstract slides |
| Andrzej Kucharski | On some properties of a base. | abstract slides |
| Ashutosh Kumar | Order dimension of Turing degrees | slides |
| Borisa Kuzeljevic | A long chain of P-points | abstract slides |
| Arkady Leiderman | Quotients of free topological groups | abstract slides |
| Marcin Michalski | Smital and Fubini among trees | abstract slides |
| Kaethe Minden | Maximality and Resurrection | abstract slides |
| Nenad Morača | Variations of reversibility | abstract slides |
| Sonia Navarro Flores | Borel ideals and Ramsey spaces | abstract slides |
| José de Jesús Pelayo Gómez | Between Hausdorff and Selective | slides |
| Veronika Pitrová | Hereditary (bi)coreflective subcategories in certain categories of semitopological groups | abstract slides |
| Grzegorz Plebanek | Small almost disjoint families and their applications | abstract slides |
| Márk Poór | Sets on the plane meeting every line in a set of measure 1 | abstract slides |
| Robert Ralowski | Continunous images of Bernstein sets | slides |
| Jonathan Schilhan | Definability aspects of ultrafilters | slides |
| Damian Sobota | On the Josefson-Nissenzweig theorem for C(K)-spaces | abstract slides |
| Šárka Stejskalová | Indestructibility of the tree property | abstract slides |
| Jaroslav Supina | On a level measure | slides |
| Jarosław Swaczyna | Haar-small sets in Polish groups | slides |
| Dorottya Sziráki | The Open Dihypergraph Dichotomy for Definable Subsets of Generalized Baire Spaces | abstract slides |
| Alessandro Vignati | Heavy lifting | abstract slides |
| Magdalena Włudecka | Products of gamma sets | abstract slides |
| Thilo Weinert | Polarised Partition Relations for Order Types | abstract slides |
| Wolfgang Wohofsky | A Sacks amoeba preserving distributivity of $P(\omega)/\mathrm{fin}$ | slides |
| Rafael Zamora | Generics in a measurable wreath product | abstract slides |
